UNIFIED SCREW THREADS AND TOLERANCES CALCULATOR (INCH)


Unified screw threads and tolerances calculator was developed to calculate basic major, minor and pitch diameters of the external (bolt) and internal (nut) inch thread according to ASME B1.1-2003 standard. In addition to basic size calculations, limits of sizes calculations of different tolerance classes can be done according to same standard.

Calculator covers :

- UN and UNR thread forms

- Standard series of UNC, UNF, UNEF, UN-4, UN-6, UN-8, UN-12, UN-16, UN-20, UN-28 and UN-32.

- Tolerance classes of 1A, 2A and 3A for bolts and 1B, 2B and 3B for nuts

- Thread size from 0.0600 inch to 2 inches

Calculations can be done by selecting a desired thread size from a list of thread sizes which are in the diameter range from 0.060 inch to 2 inches. Bolt and nut tolerance classes can be selected among the alternatives 1A, 2A, 3A and 1B, 2B and 3B respectively. Class 2A and Class 2B are selected classes for commercial external and internal threads in ASME B1.1-2003. The user shall use class 2A for bolts and 2B for nuts unless there is a specific requirement to use other tolerance classes.

Dimensions given by this calculator are at 68 °F per ASME B1.1 standard.

Unified inch screw threads basic profile is shown in the following figure.  For the design profile,  see the "General Information" section.

Note: For more information on Unified screw threads including thread form, thread series, diameter-pitch combinations, standard series and combinations, thread designation, basic dimensions and formulas, please refer to pages 1813 - 1857 of Machinery's Handbook, 29th.

The basic profile for Unified inch screw threads
Unified inch screw thread (UN and UNR) basic profile according to ASME B1.1-2003

Calculator:

INPUT PARAMETERS
Nominal Size in Inches
and Threads per Inch
External Thread (Bolt)
Tolerance Class *
Internal Thread (Nut)
Tolerance Class **

Note : * 2A is normally selected for commercial external (bolt) threads. Use this tolerance class for commercial external (bolt) threads.

Note : ** 2B is normally selected for commercial internal (nut) threads. Use this tolerance class for commercial internal (nut) threads.


RESULTS
Parameter Symbol Value Unit
Nominal Size -- --- ---
Threads per inch -- ---
Tolerance Class for External Thread -- ---
Tolerance Class for Internal Thread -- ---
Series Designation -- ---
LIMITS OF SIZES FOR EXTERNAL THREADS (BOLTS)
Allowance es --- inch
Maximum Major Diameter dmax ---
Minimum Major Diameter dmin ---
Maximum Pitch Diameter d2max ---
Minimum Pitch Diameter d2min ---
UNR Maximum Minor Diameter d3max ---
LIMITS OF SIZES FOR INTERNAL THREADS (NUTS)
Minimum Major Diameter Dmin --- inch
Maximum Pitch Diameter D2max ---
Minimum Pitch Diameter D2min ---
Maximum Minor Diameter D1max ---
Minimum Minor Diameter D1min ---
BASIC DIMENSIONS
Basic Major Diameter d , D  --- inch
Basic Pitch Diameter d2 , D2 ---
Basic Minor Diameter d1 , D 1 ---
UNR Reference Minor Diameter
 for External threads		 d3 ---
Fundamental Triangle Height H ---
Lead Angle at Basic Pitch Dia. λ --- ---


Note-1: ASME B1.1-2003 specifies limits of size that pertain whether threads are coated or uncoated. Only in Class 2A threads is the allowance available to accommodate coatings. Thus, in all classes of internal threads and in all Classes 1A and 3A external threads, limits of size must be adjusted before plating to provide suitable provision for the desired coating.

Note-2: Unless otherwise specified, size limits for standard external thread Class 2A apply prior to coating. The external thread allowance may thus be used to accommodate the coating thickness on coated parts, provided that the maximum coating thickness is no more than one-fourth of the allowance.

Note 3: The minimum diameters of Class 1B, 2B and 3B threads, whether or not plated or coated, are basic and give no allowance or clearance for assembly at maximum-material limits.


Definitions:

Design Profile: The shapes of the external and internal threads in which the limits of dimensions are applied.

Gages and Gauging : Specifications and dimensions for the gages used on Unified inch screw thread is defined in the ANSI/ASME B1.2-1983 standard. Types of gages including thread plug gages, snap gages, thread ring gages and plain diameter gages for internal and external threads are covered in same standard. Screw thread gauging systems for acceptability is covered in the ASME B1.3-2007 standard.

Major Diameter: The maximum diameter of a thread which is diameter of the crest of a male thread or root of a female thread.

Minor Diameter: The minimum diameter of a thread which is diameter of the root of a male thread or crest of a female thread.

Unified Screw Thread: A thread form used by the United Kingdom, Canada, and the United States to obtain screw thread interchangeability among these three nations. It has 60° thread angle and dimensions are stated in inch units.

UN form screw threads: The UN thread is intended for general purpose fastening operations.

UNC (Unified National Coarse): Most commonly used type for general engineering applications. This thread form is used in materials with low tensile strength which makes threads more resistance against stripping (internal threads) .UNC give possibility for quick assembly.

UNF (Unified National Fine): External threads of this Fine Series have greater tensile stress area than comparable sizes of the Coarse series. The Fine series is suitable when the resistance to stripping of both external and mating internal threads equals or exceeds the tensile load carrying capacity of the externally threaded member. It is also used where the length of engagement is short, where a smaller lead angle is desired, where the wall thickness demands a fine pitch, or where finer adjustment is needed.

UNEF (Unified National Extra Fine): Used when finer pitches than UNF are needed (Ex: Short engagement length).

UNS (Unified National Special): UNS are special series. Bolt / screw selection shall be done from standard series unless there is a special requirement to use a special series.

Thread class: A classification system to classify the threads for interchangeability and manufacturability. Class 1 threads are loosely fitting thread and used for ease of assembly. Most commonly used class is 2 and this class is designed for general use. Class 3 is used for closer tolerances.

Threads per inch: Number of full thread per an inch length.


General Information:


Some general information about the unified inch screw threads is listed in this section.

- The design profile of the unified screw thread form for classes 1A, 2A, 1B, and 2B is shown in the following figure. Refer to ASME 1.1:2003 standard for the profile of class 3A and class 3B.

The design profile for Unified inch screw threads
Unified inch screw thread (UN and UNR) design profile for classes 1A, 2A, 1B, and 2B according to ASME B1.1-2003

- ASME B1.1-2003 standard covers for UN and UNR thread forms with sizes from 0.0600 inch to 6 inch.

- The difference between UN and UNR thread forms is the form of root section. For UN thread form , the root of the thread is flat. Optionally a rounded root contour is allowed. For UNR, the root of the thread is only rounded root contour. UNR thread form is applicable to external threads only. UNR internal thread does not exist.

- The design profiles of external thread of UN and UNR screw is flat according to standard but it’s allowed to have some corner radius as shown in the figure. The same situation is valid for root of the internal threads.

- Standard series is given in the standard screw thread series table for information.

- The basic profile of UN, UNR and ISO profiles are same .

- Unified thread form and ISO metric form are not interchangeable

- In case to determine the thread pitch quickly, tools named thread pitch gauges can be used to find the pitch of the internal and external threads. Thread gauges are not used for precise measurements but allows user to determine thread pitch without losing time.

List of Equations:

Parameter/Condition Symbol Equation
Height of fundamental triangle H Equation for external thread height of fundamental triangle
Thread basic pitch diameter d2, D2 Equation for thread basic pitch diameter
Thread basic minor diameter d1, D1 Equation for thread basic minor diameter
External thread maximum major diameter dmax Equation for external thread maximum major diameter
External thread minimum major diameter dmin Equation for external thread minimum major diameter
External thread maximum pitch diameter d2max Equation for external thread maximum pitch diameter
External thread minimum pitch diameter d2min Equation for external thread minimum pitch diameter
External thread UNR reference minor diameter d3 Equation for external thread UNR Reference Minor Diameter
External thread UNR maximum minor diameter d3max Equation for external thread UNR Maximum Minor Diameter
Internal thread minimum major diameter Dmin Equation for internal thread minimum major diameter
Internal thread maximum pitch diameter D2max Equation for internal thread maximum pitch diameter
Internal thread minimum pitch diameter D2min Equation for internal thread minimum pitch diameter
Internal thread maximum minor diameter D1max Equation for internal thread maximum minor diameter
Internal thread minimum minor diameter D1min Equation for internal thread minimum minor diameter

List of Parameters
Symbol Definition
es Allowance
Td Major diameter tolerance of external thread
Td2 Pitch diameter tolerance of external thread
TD1 Minor diameter tolerance of internal thread
TD2 Pitch diameter tolerance of internal thread

Reference:

  • ASME B1.1-2003, Unified Inch Screw Threads (UN and UNR Thread Form)
  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc.
  • Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc.